Stability of solutions to nonlinear diffusion equations

Teemu Lukkari

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arXiv · 1206.2492

Stability of solutions to nonlinear diffusion equations

Teemu Lukkari

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Abstract

We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit problem with the same data as $m$ varies. Our arguments are elementary and based on a general principle. We use neither regularity theory nor nonlinear semigroups, and our approach applies to e.g. Dirichlet problems in bounded domains and Cauchy problems on the whole space.

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Teemu Lukkari. 2013-09-03. Stability of solutions to nonlinear diffusion equations. https://arxiv.org/abs/1206.2492

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